The Convolution Theorem in 2D

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Paz INBAR
Paz INBAR 2021-5-16
回答： Sulaymon Eshkabilov 2021-5-19
Hello,
I have two images A and B with different size.
I want to show that:
fft2(conv2(A,B))
is equal to
fft2(A).*fft2(B)
but I get different outputs.
what is the problem?
Thanks.

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回答（3 个）

Matt J
Matt J 2021-5-17
编辑：Matt J 2021-5-17
Ran in:
The problem is that you need to zero-pad,
A=rand(10); B=rand(10);
szA=size(A);
szB=size(B);
szFull=szA+szB-1;
result1 = fftn(A,szFull).*fftn(B,szFull);
result2= fftn(conv2(A,B,'full'));
difference=norm(result1-result2,'inf')
difference = 1.0735e-12
Jonas
Jonas 2021-5-17
编辑：Jonas 2021-5-17
i suggest you have a look onto file exchange, there is an example called 2d convolution theorem
https://de.mathworks.com/matlabcentral/fileexchange/60897-2d-convolution-theorem
  1 个评论
Paz INBAR
Paz INBAR 2021-5-17
Thank you for your answer.
I ran this file but I got different images in R ( I*M ) and in R ( ifft(F X W) ) , according to names of the images in this file.
(which are the both sides of the convolution theoren).

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Sulaymon Eshkabilov
Note that the sizes of A and B must match. In your inserted image array, sizes of A and B must have differed.

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